Question

Barb the baker has developed a new temperature scale for her bakery called the Breadus scale, which is a linear function of the Fahrenheit scale. Bread rises at $110$ degrees Fahrenheit, which is $0$ degrees on the Breadus scale. Bread is baked at $350$ degrees Fahrenheit, which is $100$ degrees on the Breadus scale. Bread is done when its internal temperature is $200$ degrees Fahrenheit. What is this in degrees on the Breadus scale?

$33$

$34.5$

$36$

$37.5$

$39$

Solution:

The Breadus reading is linear in Fahrenheit through $(110, 0)$ and $(350, 100),$ so $B = \frac{100}{350 - 110}(F - 110) = \frac{5}{12}(F - 110).$ Plug in $F = 200:$ $B = \frac{5}{12} \cdot 90 = 37.5.$ Therefore, the answer is D.

2023 AMC 10A Problem 8

Solution:

Problem 8 in Other Years